You act as if disregarding the self-report component is minor, but surely it is fundamental.

The original theory is that bullying is a way for someone with low self-esteem to make themselves feel superior. By the definition of the theory, a bully so motivated not to see themselves as having low self-esteem that they will resort to violence. Someone who will resort to violence to avoid acknowledging something, is unlikely to self-report accurately on that same topic.

Self-report is therefore clearly an invalid measure by which to test this theory.